Method of producing gears



May 23, 1950 E. WILDHABER 2,598,556

METHOD OF PRODUCING GEARS Filed Oct. 25, 1944 3 Sheets-Sheet l L/S E7. 4

' ISnveutor Big. 2 5 ERNEST WHLDHABBR (Ittorneg May 23, 1950 E WILDHABER METHOD OF PRODUCING GEARS 5 Sheets-Sheet 2 Filed Oct. 25. 1944 5 attorney May 23, 1950 Filed Oct. 25. 1944 E. WILDHABER 2,508,556

METHOD OF PRODUCING GEARS 3Sheets-Sheet 3 fly/l 12 3/40 0 Summer Patented May 23, 1950 UNITED STATES PATENT OFFICE METHOD OF PRODUCING GEARS Ernest Wildhaher, Brighton, N. Y assignor to Gleason Works, Ro hest r, N- a rp r tion of New York The present invention relates to longitudinally curved tooth bevel gears and to methods for proucine s ch ar In the spur gearfield, the involute is the best known and most widely used form of tooth. A primary advantage o. f the involute tooth shape over other tooth shapes in this field is that. the center distance, or the distance between the parallelv axes of two mating gears may be varied without affecting the. motion transmitted. A pair of involute spur gears. will continue to transmit'nniforrn motion at any center distance so long as enough of, the tooth surfaces of the two gears remain, in enga ement to, transmit motion.

Involute bevel gears have. a characteristic analog 'ous to that of the involute spur gears. The. angle between the axes of two mating involute. bevel gears may be varied without loss of uni-. form ty of motion and without shift of the tooth bearing. or contact. other words, one. member f. an. involute bevel sear pair may be shift d. about the common apex. oi the twov gear so that its axis h s a difierent shait an le with the. axis of the mat gear without affecting the correctness of the gear me hr Another charact ri tic oi ma ng in olute bevel. gears is that the gear ction or tooth contact takes. place n. the. opposite sides of th teeth in. wo pl n w ic inters'ec lo g the common pi ch l me t f th wopi ch cones of th scars and which re. nsent" to th ase nes or t e gea Cons quently, the two matin gears. will have constant. transverse. pressure ngles a l lo e the lengt s f their teeth. A. truly involut oot s r ce,

then, can h describe n. bevel gear by a lin in he. plane ang nt to th s on wh n th t plane is unwrapped from or wrapped about. the bas one.

Hcrctoiore, n s isfa t ry e o has exi t d for enerat n invo ute. spiral b vel sea In prior attempts to nerate such gears, a tool o zerojpxessure .angleha been us d and the to th surfaces of. a scar have been p duced by rollin thet ol and ear blank together on the base cone f. the. blank with a constant rati of n rating roll; This method has several distinct. disa v nrases. par icularly when the zero pr s ure an l toolis. or annula form, suitable for pr ducin ongi dinally curved. tooth bevel gears. Thus. if

' he tool is. an. annular grindin wheel, it. is not at all practi al. ior i cylin rical grinding surface; anno be dr ssed without. changing the diameter oi the tool. On he, other hand if the oo a race mill cutten, the blades have to. be

adiusted radially oi the. cu ter axis. after shar 2 eningr. This is a tim -consum n as d d iii cult to perform accurately. Further, oftentimes the. choice of pressure angl to be used on the teeth. of the gear; which is to be cut or ground is limited when gears of large pitch angle are involved, for the base cone should be outside of the root cone of a, gear especially in the case of bevel gears having teeth of positive spiral angle, and this is not always possible when annular tools of zero pressure, angle are to. be emplayed for the cutting or grinding of the. gears... Still further, by any process heretofore known, both sides of the teeth of involute bevel gears cannot be generated simultaneously on both members of the gear pair with an annular cutter or wheel. Moreover, even Where the two sides. of a tooth space are cut. simultaneously on one member of the gear pair only, difliculties are en.- countered. Thus an unduly large generating roll must be employed, at, least in the production of the ring gear or larger member of the bevel gear pa r. In addition, Where the two sides of a tooth space are. cutv imultaneously, they corre-. spond to concentric circles in the base cone development of the gear. In other words, the, tooth pa e in t base cone. has a c nstant width whereas it should ordinarily taper in width from one end of the tooth space to the other, larger at the outside end of the tooth space and smaller at the inside end. The result is that when both sides of the tooth spaces are cut simultaneously on one. member of the bevel gea pair, th t oth sp es. of the mating gear m mber are required to have excessive taper.

practical to cut. one side. of. the teeth at a time. on both member of the ear pair. Ii this is necessary, a very material increase in pro uction time for the involute bevel gear pair results as coma pared with he produ tion times .for vel gear pairs of other than involute tooth shape. For. all of these reasons, involute bevel gears haye.

for producing longitudinally curved tooth bevel Sometimes, this requ red tapcris so excessiv that it m y be m re.

bevel gears simultaneously on oneor both members of a mating gear pair.

Still another object of the invention is to provide longitudinally curved tooth involute bevel gears having correct taper in width of their tooth spaces and suitable pressure angle;

Other objects of this invention will be apparent hereinafter from the specification and irom M the recital of the appended claims.

In cutting bevel gears according to the process of the present invention, an annular cutter or grinding wheel of positive pressure angle is employed. The axis of the tool is inclined to the blank so as to cut tooth spaces in the blank which taper. in depth from their inner to their outer ends, and to avoid bias bearing, a cutter or grinding wheel of spherical or approximately spherical form is employed. Generation is eifected by rolling the tool and work together as though the gear being out were rolling on a basic gear having a pitch angle of other than 90. In the prferred embodiment of the invention the tool and work are rolled relative to one. another during generation as though the Work were rolling with an internal tapered gear represented by the stool and the ratio of relative roll of the tool and work is varied during generation. Thus, both sides of each tooth space of the work may be cut simultaneously to the desired profile shape.

Because of the use of a positive pressure angle tool, there is no change in the diameter of the tool after sharpening or dressing. Moreover with the present method, there is no limitation as to the pressure angle which may be employed in the gears to be cut. Further than this, with the method of the present invention, the base cone does not have to be ouside the root cone; it may be well within the root cone. Neither does the root cone have to be parallel to the base cone. With the method of the present invention, moreover, both sides of a tooth space may be generated simultaneously on one or both members of the gear pair.

In the drawings: c

Fig. 1 is a fragmentary view of a bevel gear made according to this invention in development, or of a basic crown gear such as may be used in the production of this bevel gear, and illustrating diagrammatically certain of the principles on which the present invention is based;

Fig. 2 is a view, partly in section, of a pair of involute spiral bevel gears produced according to this invention; 1

Fig. 3 is a sectional view, along the line 3-3 of Fig. .2, furtherillustrating the construction of these gears;

Fig. 4 is a sectional view, along a line corresponding to the line 33 of Fig. 2, showing a tooth of the basic gear or a blade of a cutter such as may be employedin the production of longitudinally curved tooth involute gears according to this invention, and further illustrating the principles on which the invention is based:

Fig. 5 is a diagrammatic view illustrating the production of the pinion or smaller member of a bevel gear pair according to this invention;

;. Fig. 6 is a diagrammatic view illustrating the of the pair;

Fig. 7 is a fragmentary developed sectional view of a spiral bevel pinion generated according to the invention and having longitudinally curved teeth of positive spiral angle;

Fig. 8 is a fragmentary developed sectional view of the mating spiral bevel gear;

Fig. 9 is a fragmentary developed sectional view of an involute bevel gear made according to this invention having longitudinally curved teeth of zero spiral angle; and

Figs. 10 to 12 inclusive are diagrammatic views illustrating different positions of a cutter and gear blank in the generating roll during simultaneous cutting of thetwo sides of a tooth space of a gear by the preferred method of the present invention.

In the drawings, l0 and II denote, respectively.

the pinion and gear of a mating spiral bevel gear pair produced according to this invention. The axes of these two gear members are at l2 and I3, respectively, and intersect in the common apex M of the pair. face of thepinion rolls on the conical pitch surface of the gear and these pitch surfaces contact crown gear, that is, a crown gear having a pitch angle of 90 and an axis at I! perpendicular to the pitch line It, then the two members of the Y pair will have correct and full match, provided that the crown gear used in generating one member is the exact counterpart of the crown gear used in generating the other member. These crown gears may be provided with spherical tooth sides because this permits cutting the gear and pinion withtapering tooth depth without departure from mathematical accuracy. Thus, the crown gear used in generating the gear ll'ma'y contain teeth l8 whose opposite sides I9 and 26 are spherical surfaces whose centers .are at 2| and 22, respectively. Such a crown gear tooth can readily be represented by an annular cutter v or grindin wheel whose axis 23 (Fig. 4) passes through the two sphere centers 2| and 22. An axial section of the grinding wheel or of a blade of such a cutter is denoted at 25 in Fig. 4. 0pposite sides of the grinding wheel or cutter are denoted at 21 and 28, respectively. The centers of these sides are at 2! and 22, respectively.

In the conventional method of generating a bevel gear. rolling motion is effected by rotation of the work. such as gear II, on the work axis 13 while relative rotation is produced between" the cutter and the work about the crown gear ax s I! so that the pitch cone of the work rolls without sliding on the pitch plane of the crown gear. Assuming that during generation these two axes remain in fixed positions, the sphere centers 2! and 22 will then move in circular paths M and 2 respectively, about the crown gear axis H. In Fig. 4. these circles appear as straight lines. Thus, if the bevel gear H were to be generated by the usual method of generating ordinary bevel gears with a spherical cutter, the center ,2! of one side of'the cutter would move during generation to position 2| while the cen-j ter. 22 of the other side of the cutter would move from 22 to'position 22'. In the posltions Zl' and 212" of the cutter centers, contact between the sides of the cutting tool and the work willbe in a plane containing the instantaneous axis It In mesh, the conical pitch sur gamete and the sphere centers 2M or '22, respectively, which means that th transverse pressure -angle of the work would be changed.

To obtain invol'ute teeth, however, the-sphere centers should move in theplanes of action, that is, in the planes 29 and 30 respectively (Figs.v 3 and 4=)-, tangent to the base cones of the gears: and intersecting the instantaneous axis l6. That: is, the sphere center 2t should move during generation in the plane- 25 to a position '2-'l"-""' while I the sphere center 22 should move in the plane 36* to a position 22""; Inother words, asuthe sphere center turns about the axis t? through an angle to position 2|, it should also turnaboutthe instantaneous axis I 8- to moveit from It to 21 so that the resultant path of its movemerit should be from '2l' to '2 l Bikewise, the other sphere center should move in. a resultantpath 22 to 22.

Let H and V'denote the coordinates ofthe-po'int 21 in the view' of Fig. i and let Q denote-the angle on the circle 24 between the point Hand the axial plane 11-43. Then,

Distance 2i--2'l', as it appears in the projection of Fig. 4, is then for infinitesimal displacement through an angle 9 equal to H -H,. the angle 0 being measured in radians.

The angle 2l"'-2'l- 2'f"' (Fig. 4) equals the. known transverse pressure angle (p for oneside of the gear. Hence, the. distance 21 -21 should. be, equal to:

Hence:

11 ctn G) =H6-sin qt 00805 whence;

The. above formula is obviously applicable to the other side of the tooth also if the angle 1 -14-22 of Fig. 1 is introduced as Q and the transverse pressure angle (p is introduced as a negative quantity for that side. The coordinates H and V for th point 22 must. also be used.

Invo'lute teeth may then be obtained by generating one side of the teeth of the gear ll from a basic gear having an axis 32 (Fig. 2') and whose pitch angle is less than 90. The other side of the teeth of gear H. should then be generated from a basic computed as above described and having a pitch angle larger than 90; 32" de notes the cf such a gear. The mating sides of the other member of the gearpai'r may be gen-' erated from two basic gears which are counter,-

of the aforesaid basic gears and'whieh'have on the axis 32.

thesameaxes. 32 and: 32'; respectively; During; generation of the sides of the teeth ofr'both gear and pinion, the: ratio. of roll will :be, of course, constant, that: is, thework will, rotate units: axis at a uniform velocity while. work and, tool are moved relative to one. another about the axis. of the basic gear also at a uniform velocity.

When cutting the longitudinally concave sides of the teeth of the gear H with the outside spherical cutting surface. 2T of the cutter, the basic gear hasits axis at 32 and a pitch angle, Gsmaller than 9'0. The mating longitudinally convex tooth surfaces: of the pinion ID are, then generated from a basic gear having the same axis 32 and a pitch angle G equal to 180 minusG and, there.- iore, larger than When generating the con.-

vex lengthwise tooth sides of the gear ll withv the inside spherical cutting edges .28 of the cutter, the'basicgear has an. axis: 32 and a. pitch angle- G1- larger than 90. The mating longitudinally concave tooth surfaces of the pinion are then gen.- erated from a basic gear having the same. axis 32" and a pitch angle G2 equal to 1'80--G1, namely, smaller than 90.

The pitch angles of the basic generating gears, thatis', the positions of the axes 32 and 32" may also be obtained by erecting a normal to the plane iii-2t (Fig. 4) at point 21. "This normal intersects the axial plane I'2-- l3 in a point lying the point 22 to the plane l t-22 intersects the axial plane l2l3 in a point lying in the axis 352'. When the sphere center 21' is moved about an axis 32 determined in this manner, it. is bound to move in a circle tangent to the plane Iii-4|, and likewise, the sphere center 22 is bound to movein a circle tangent to the plane |'6--22 when the sphere center 22 moves about axis 32". The above formula can b considered as an expression of this relationship. Fig. 3' shows intermesh'ing teeth of the pinion Ill and gear II. On truly involute gears, mesh takes place in the two planes- 29 and 30 which intersect at instantaneous axis. i6 and which are tangent to the base cones 34 and 35 of the two gears. These base cones are coaxial with the axes l2 and i3, respectively. It is to be noted that in the case shown, the base cone 35' is within the root surface of the teeth of the gear H Contact between the mating tooth surfaces of the gear and pinion is along a line which for one side of the teeth, moves duringmesh about an axis 36' perpendicular to the planeof action 30 and passing through the common apex l4. Involute gears can be described, simply and completely by development of the base cone to a plane, which shows the nature and position of said line of contact, and by' the angle between the axis of the gear and the elements of the base cone.

A pair of gears produced as described conjugate to an externally and an internally tapered basic gear having spherical tooth surfaces, respectively, will transmit mathematically accurate uniform motion. The tooth shape of the gears is a close approximation of a true invol-ute shape. For all practical purposes, namely, for purposes of adjustment, the gears so produced are involute gears. They have a constant transverse pressure angle and permit variation in the angle between the axes of the two gears. It is to be seen that the angles G1 and G differ from 90 and from each other increasingly the more the angle Q, averaged for the two sides, differs from 90. With Q averaging 90", both angles are very close to "90. Where the angle Q averages 90, the gears have Likewise, a normal erected: at:

7 the same spiral angle at the large and small ends of the teeth.

With the above-described general method of generation, the tooth sides of the teeth of each member of the gear pair must be generated from different basic gears and only one side of the teeth can be cut at a time.

The preferred method of generating gears according to the present invention, however, is a process in which both sides of a tooth space of one or both members of the pair may be generated in the same operation.

Heretofore variation in the ratio of generating roll has been employed in the production of bevel gears for various purposes, as, for instance, to vary the tooth profile shape produced. I have discovered that by employing variation in the ratio of roll, both sides of a tooth space of an involute bevel gear can be generated simultaneously. The variation in ratio of roll permits of compensating simultaneously for an externally tapered basic gear and an internally tapered basic gear, so that correct tooth profiles can be produced on both sides of the tooth space with the same modification in ratio of generating roll.

It is well known that pinions conjugate to a form-cut externally tapered gear may be cut by, moving the cutter in a plane tangent to the root surface of the pinion while varying the ratio of generating roll between cutter and pinion, but the variation in ratio of roll has to be reversed for the two sides of the teeth. Using the same modification in ratio of generating roll on both sides of the teeth would make one side conjugate to an'externally tapered gear and the other side conjugate to an internally tapered gear. That is precisely what is needed here and that is whatis employed. Modification in the ratio of roll acts faster when compensating for a basic gear of external taper than for a basic gear of internal taper. Hence, for the purposes of the present invention it is necessary to employ modification in the ratio of roll in combination with an internally tapered basic generating gear.

Fig. illustrates the preferred method of generating the teeth of the pinion Ill. The cutting tool here employed is an annular grinding wheel 25 having outside and inside spherical grinding surfaces 21 and 28, respectively, of convex and concave profile shape, respectively, whose centers are at 2| and 22, respectively, on the wheel axis 23. The wheel is tipped as shown. Generation of the tooth surfaces is effected by rotating the wheel 25 'on its axis 23 in engagement with the pinion blank l0 while rotating the work on its axis l2 and effecting relative rotational movement between the tool and the work about the axis 40 of the generating gear. The pitch angle Go, of this generating gear exceeds 90. During the generating roll, the ratio of rotation of the work on its axis l2 to the relative rotary movement about the basic gear axis 40 is modified. The amount of variation in ratio of roll is such as to obtain tooth shapes on opposite sides of the tooth surfaces such as might be produced by generating these same tooth surfaces one side at a time with uniformratio of roll and conjugate to an externally and an internally tapered basic gear, respectively. The pitch line of the generating gear is denoted at 4].

The tooth surfaces of mating gear ll may be generated with the same annular grinding wheel 25 again tipped relative to the work. In the generating operation, the wheel is rotated on its axis 23 while the work is rotated on its axis I3 the modification in ratio of generating roll when generating opposite sides of a tooth space of either gear or pinion simultaneously conjugate to.

an internal tapered gear. Here the generation or opposite sides of a tooth space of the pinion is shown specifically. The views are in the back cone developments. Hence the pinion and basic generating gear appear as though they were spur pinion and internal spur gear. e

In the embodiment of the invention illustrated in Figs. 10 to 12 inclusive, it is assumed that the work rotates on its axis 12 at a uniform velocity during generation while thecutter moves at a varying velocity about the axis 40 of the generating gear. The uniform motion of the blank combines with the varying motion of the cutter to produce the required variation in ratio of generating roll. In the generating operation the tool 25 represents, of course, a tooth of the generating gear. The tip surface of this gear is denoted at 44.

Figs. 10, 11, and 12 show corresponding positions of the tool and work for equi-spaced positions of the work as it rotates on its axis l2. Were the tool to move during generation at a uniform rate about the axis 48 of the generating gear, it would move from dotted line position 25a, shown in Fig. 10, to full line position 25b, shown in Fig. 11, while the work was simultaneously rotating about its axis l2 at a uniform rate from its position Illa of Fig. 10 to its position "lb of Fig. 11, and the tool would move from position 256 of Fig. 11 to dotted line position 250 of Fig. 12 while the work was moving from position "lb of Fig. 11 to position "3c of Fig. 12. The tooth profiles, which would be generated on opposite sides of a tooth space during such uniform roll of tool and work together, would be such as are shown in dotted lines at Ma and 48a, respectively, in Fig. 11. These profiles are unsymmetrical and are not true involutes.

With the method of the present invention, however, the tool moves at a non-uniform rate about the axis 40 of the generating gear as the work rotates at a uniform rate on its axis l2. Thus, with the present invention, the tool occupies full-line position 25 instead of dotted-line position 25a when the work is in the position [0a of Fig. 10, and the tool occupies full-line position 25" instead of dotted line position 25c when the workis in the position Inc of Fig. 12. In other words, with the present invention the tool moves from position 25' to position 2522 to position 25" at a non-uniform rate while the work is rotating at a uniform rate from position Hla' to Hlb to Illc. Thus the tool may generate simultaneously opposite side tooth surfaces 41 and 48 which are of true involute profile shape. It will be noted that the profile 4! is less curved than profile 4111 while profile 48 is more curved than profile.48a. The profiles i1 and 48 are symmet- V rical and may be involutes.

In Figs. 10, 11, and 12, the lines 58 and 59 are lines drawn radially from the work and basic gear axes l2 and 40, respectively, and median of the tooth space of the work and tooth of the basic mos as eanfrespectively The-l til' isa line connecting -the work and "basic gear axes. In Figs; and 1 2, the differences be'i'iween the dotted-line positionsofthe tool 'for uniform ratlo'of "roll easing-oh at the ends 1 of the gear teeth 'a'ndat thetops and "bottoms of' the tooth pr'o'files is "desired. $uch ease 'off smatch-can bep'fodu'ed *by application b elk-known principles, among which'are the "use of "a 'sl ightly larger radius on the outside sphericaT-suriace" of-'-the cutter than-on tl'iei'nside' spherical surface. Primarily, this causes lengthwise mismatch of the mating tooth surfaces with anease-off oi the tooth contact at the ends of theteeth. Ease-on of the contact at the upper and lower-ends of-the tooth profiles may be obtained by using a cutter whose outsidecu'ttin'g" surface has a profile less curvedthan a spherical profile and whoseinsi'de ing -sluriface-hasaprofile more curved-titan sph'e ricalprofile. v g Y Y 7 j Figs.- 7 a-nd 8a-re developments to a plane ofthe fbase-cor'ie of the pinion ll] "d gear Hi specftively. The teeth--of-the pmron are dr-iote d at if anld'the teeth of -t-he g earja 45. The "s'i'des"- "-of the pinion teeth arecarved lengthwise alohg circular arcs 4! and 48, while the mating tooth sides of the gear are curved lengthwise along circular arcs 1 and 48. Opposite sides 41 and 48 or 41' and 48 of a tooth space are inclined to one another and the tooth space tapers from end to end. The tooth bottoms or root lines 49 and 5|! (Figs. 5 and 6) are inclined to the base cones 34 and 35, respectively, and when extended ordinarily pass outside of the cone apex M, at least on gears cut duplex, that is, out two sides of-the tooth spaces simultaneously on both members of the gear pair.

Fig. 9 is a development to a plane of a base cone of a zero spiral angle gear 52 out according to the present invention. Ihe apex of this gear is denoted at 53 and its projected axis at 54. Its teeth are designated at 55 and the opposite sides of the teeth are curved longitudinally along circular arcs as denoted at 56 and 51. Here the teeth are of zero spiral angle at the center of the tooth length, that is, the sides of the teeth are tangent to lines radial of the gear apex at points midway of the length of the teeth. As in the previously described embodiments of the invention, the tooth spaces of this gear taper in width from end to end, being larger at the outer ends of the teeth, and, as in the previously described embodiments of the invention, the root lines of the teeth are inclined to the base cone.

While the process for cutting mating gears illustrated in Figs. 5 and 6 has been described in connection with the production of longitudinally curved tooth gears of involute form, it is to be understood that the idea of employing variation in the ratio of generating roll in conjunction with generation from a tapered basic gear has a broader application, and that it may be employed may, engagement with the work tvhile'- effe'cting a relative hrolling em otiom between-the *"tool and woi'k' ias though*tl'ie work were rolling for various 'othi' purposes." '--It provides aameans --fo'r =altering"- the 'iadiiustment' 'charactenistics of agenerated bevelgears to s-uit "various =;purmses and wishes while retaining thehigh production "-"of"the'vduplex method.

A's already -'=-indicated, gears -may be cut" or ground by thepresent invention and '--'since =a grinding wheel is simplya' cutt-er having an in finite nunrber of =clit-tir1g edges, the -term"= cutter as =used-=ifereinarter n the claims-will-be under stood to include a grnding'wheel, and likewise ii-heterm "butting" edge be understoodto include the *operating profile or surface of -a grinding wheel.

It *will be --further understood that'while'the invention has-been describedin connection with "particular embodiments thereof, 'it 'is capable of istill furtner modification and'this applicaticnas intended 'tO coVerai-iy variations,--uses, or adaptatio'n's of --the invention,-'-= followingfi in general, the principlesof-the inventicn-and including such departures dramthe-represent disclosure as "eomewithin known or 'customary practice in the g'ear -art'"and as-inay be' appl'ie to the essential features" hereinbefo're' 'set forth an'd as fall withthe scope of 'the invention orthe i Iimi-TJS'FOI t e" appended -'clai-ms.

Y i laiving thos idescribed"my rlnventiomwhat a! claim is:

method of lgner'ating tooth-(surfaces inally'curvedtooth bevelrgear which ofeach 'ofwits tooth on an internal tapered gear represented by the tool, and varying the ratio of the rolling motion during generation.

2. The method of generating a bevel gear which comprises cutting opposite sides of its teeth by positioning an annular tool, that has side-cutting edges of circular arcuate profile shape, in engagement with the work so as to cut tooth surfaces tapering in depth from end to end, and rotating said tool in engagement with the work while effecting a relative rolling motion between the tool and work as though the work were rolling with a basic gear, represented by the tool, the basic gear employed during generation of one side of the teeth being an externally tapered basic gear and the basic gear em ployed during generation of the opposite sides of the teeth being an internally tapered basic gear.

3.. The method of generating a bevel gear which comprises cutting both sides of its tooth spaces simultaneously by rotating an annular tool having outside and inside cutting edges of circular arcuate profile shape in engagement with the work while effecting a relative rolling motion between the tool and work as through the gear, which is being out, were rolling with an internal bevel gear represented by the tool, and varying the ratio of the rolling movement during generation.

4. The method of generating a pair of bevel gears which comprises cutting both sides of each tooth space of each member of the pair simultaneously by rotating an annular tool, which has outside and inside cutting edges of circular arcuate profile shape, in engagement with the work while effecting a relative rolling motion fb'etween the tool and work as though the gear, which is being cut, were rolling with a generating gear represented by the tool whose pitch tooth space of each member of the pair simultaneously while rotating an annular tool, which has outside and inside cutting edges of circular arcuate profile shape, in engagement with the work while efiecting a relative rolling motion between the tool and work as though the gear, which is being out, were rolling with a gear.

which is represented by the tool, whose pitch angle is greater than 90, andvarying the ratio of the rolling movement during generation.

6. The method of cutting opposite sides of a tooth space of a tapered gear simultaneously which comprises imparting a cutting motion to a tool while effecting a relative rolling motion between the tool and work as though the work were rolling with atapered gear represented by the tool which has a pitch angle of more than 90, the ratio of the rolling motion being varied during cutting.

'7. The method of cutting opposite sides of a tooth space of a, tapered gear simultaneously which comprises positioning an annular tool, that has inside and outside cutting edges of concave and convex profile shape, respectively, in engagement with the work with the axis of the tool inclined at other than right angles to the pitch surface of the work so as to cut a tooth space tapering in depth from end to end, and

12 rotating the tool while effecting a relative rolling motion between the tool and work as though the work were rolling with an internal tapered gear represented by the tool which has a pitch angle of more than and varying the ratio of the rolling motion during cutting.

8. The method of cutting a pair of tapered gears which comprises cutting opposite sides of each tooth space of each member of the pair; simultaneously with an annular tool, that hals inside and outside cutting'edges of concave. and convex profile shape, respectively, by position-' ing said tool in engagement with the work with the axis of the tool inclined at other than right, angles to the pitch surface of the work so as cut a tooth space tapering in depth from end to end, and rotating the tool on its axis while rotating the work on its axis at a uniform velocity and simultaneously effecting relative rota! tional movement between the tool and work at a varying velocity about another axis which is inclined to the pitch surface of the work at an angle greater than 90.

ERNEST WILDHABER.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS 

